Normal forms of quadratic vector fields and the Shi Songling equation
type: Item
instance of: scholarly article
title: Normal forms of quadratic vector fields and the Shi Songling equation
zbMATH Open document ID: 1218.34032
DOI: 10.1134/S0012266110050046
author: D. A. Filimonov
published in: Differential Equations
publication date: 2010-12-08T00:00:00Z
review text: The paper contains a method for the localization of limit cycles for planar vector fields with a weak focus. This method is applied to analyze a large domain on the phase plane for the Shi Songling example -- a quadratic vector field with at least four limit cycles. In a neighborhood of the singular point \(O(0,0)\) three very narrow annuli are obtained in each of which there is a unique limit cycle.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 5824114
zbMATH Keywords: quadratic system
zbMATH Keywords: limit cycle
zbMATH Keywords: bifurcation
zbMATH Keywords: Hilbert's 16th problem
Wikidata QID: Q115252546
MaRDI profile type: Publication
cites work: On hereditarily indecomposable Banach spaces
cites work: Q3868118
cites work: On the distribution and number of limit cycles for quadratic systems with two foci
cites work: Q5434578
full work available at URL: s0012266110050046
OpenAlex ID: W2149212478
description: scientific article; zbMATH DE number 5824114